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Chapter 1: Problem 201

Simplify. $$ 8|-7| $$

Short Answer

Expert verified
56

Step by step solution

01

Understand the Absolute Value

The absolute value of a number is its distance from zero on the number line without considering direction. So, \[ |-7| = 7 \]
02

Multiply the Results

Now, multiply 8 by the result of the absolute value. So, \[ 8 \times 7 = 56 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. This means whether the number is positive or negative, its absolute value is how far it is from zero. For example, \(|-7| = 7\). This is because -7 is 7 units away from zero. In short, the absolute value ignores whether a number is to the left or right of zero on the number line.
Multiplication Involving Absolute Values
Once the absolute value of a number is determined, multiplication follows normal arithmetic rules. For instance, in the problem \(8\| -7 |\), the absolute value of -7 is found first: \( |-7| = 7\). Next, multiply 8 by this result: \( 8 \times 7 = 56 \). Multiplying after finding the absolute value ensures that only positive distances are considered in calculations involving absolute values.
Absolute Value on the Number Line
Imagine the number line, a horizontal line with zero in the middle. Numbers to the right of zero are positive, while numbers to the left are negative. Absolute value measures only the distance from zero, ignoring direction.
\(7\) is 7 units to the right of zero, so \(|7| = 7\). \(-7\) is 7 units to the left of zero, so \(|-7| = 7\). This concept simplifies how we work with numbers and their distances, especially in calculations.

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